Mixing between a reference signal and a data signal is often necessary to extract information about an optical device or network. A probe signal and a reference signal originating from the same source are typically mixed, resulting in fringes that can be detected and used to assess information about the device being probed. In interferometric sensing, a reference signal is mixed with a signal whose phase and/or amplitude is modified by a parameter to be measured. The mixing produces an interference signal, and the amplitude of the interference signal depends on how efficiently the two optical signals mix.
Optical Time-Domain Reflectometry (OTDR) is a widely used tool for identifying problems in large optical networks. OTDR instruments provide measurements of the level of scatter present in a section of fiber, or at a discrete interface over long distances. Optical Frequency Domain Reflectometry (OFDR) may be used to provide data similar to that provided by OTDR over shorter ranges (tens of meters for OFDR instead of 1000's of meters for OTDR) and higher resolutions (tens of microns for OFDR instead of tenths of meters for OTDR). This change in distance scale allows OFDR to be used in applications where the dimensions of interest are centimeters instead of meters such as when optical coupler and switch networks are constructed. For example, OFDR may be used in module-level and sub-module-level diagnostics. The above-identified related application explains how an OFDR can be used to measure the complex spectral reflectivity of Rayleigh backscatter as a function of fiber length and how that can be very useful in a number of applications.
Scatter is the process of redirecting the propagation of light. In an optical fiber, this occurs when light encounters a change in the geometry of the fiber core, or a change in the local index of refraction of a fiber. Scatter generally occurs at any interface such as connectors, poor splices, collimating optics, etc. Typically, light scattered from the forward propagating direction into the backward propagating direction is of primary concern and is called a reflection. Rayleigh scatter, in the context of optical fiber, describes the light scattered in the fiber due to the random nature of the glass structure in and around the fiber core. Although Rayleigh scatter is random in nature, it is fixed because the random pattern of the glass structure is “frozen” into the fiber. Scatter is a form of loss, and loss is the removal of light from the intended propagating mode.
Bragg gratings have been used to measure the “beat length” (which is different from “beat frequency”) of a polarization maintaining (PM) fiber. FIG. 1 conceptually illustrates beat length. A polarization maintaining (PM) optical fiber 1 includes two stress rods 2a and 2b and a waveguide core 3. Light propagating along the core 3 includes two perpendicular polarization vectors, commonly labeled “p” and “s”. These perpendicular polarization vectors correspond to two perpendicular electromagnetic (EM) fields (only the electric fields are illustrated to simplify the figure and demonstrate the principle). To be a PM fiber, coupling between the two EM fields needs to be minimized so that energy from one polarization/field “mode” is not transferred to the other polarization/field “mode”. That mode coupling decreases as a phase velocity difference between the two polarizations/fields increases. Phase velocity is described in more detail below.
The stress rods 2a and 2b, which have a different thermal coefficient and index of refraction than the core 3, create a phase velocity difference between the two polarizations/fields. The “fast” electric field shown as the thicker sine wave corresponds to a “fast mode,” and the “slow” electric field shown as the thinner sine wave corresponds to a “slow mode.” The fast mode and slow mode light waves have different phase velocities. The light in the fast mode will have a longer wavelength than the light in the slow mode. As a result, the two electric fields change in phase relative to another as they propagate down the fiber. The two fields start in phase, and then after changing phase by 360 degrees over a certain distance along the fiber, they are back in phase. The distance over which this phase realignment takes place is the “beat length.”
The beat length is a useful parameter to measure for a PM fiber or other optical device because it represents the degree of polarization coupling, (which is usually undesirable), in that PM fiber. A shorter beat length means less mode coupling and a better PM fiber. But beat length should not be confused with a difference in group velocities. As shown in FIG. 2, when two closely spaced wavelengths are present, they form “beat-notes” in each of the modes of the PM fiber corresponding to the envelope waveforms as opposed to the underlying higher frequency waveforms that create the envelopes. The slow and fast envelopes propagate down the fiber at different group velocities. These group velocities can be substantially different from the phase velocities that create the beat length.
Birefringence and beat length are related, and one can be readily calculated from the other. For purposes of this description, the birefringence is used to describe the property to be determined for a PM fiber. A birefringent material causes different light polarization modes to travel at different speeds through the birefringent material, and birefringence is the degree to which a light wave with two polarizations is split into two unequally reflected or transmitted waves when it travels through a birefringent material. More formally, birefringence, Δn, is given by:nslow−nfast=Δn  (1)where nslow and nfast are the refractive indices for the slow and fast propagation modes, respectively. The beat length d is related to birefringence in accordance with the following:
                    d        =                  λ                                    n              slow                        -                          n              fast                                                          (        2        )            where λ is the nominal operating wavelength (in a vacuum), e.g., a center wavelength of operation of system where the PM fiber is incorporated or the design wavelength of the fiber.
A Bragg grating can be used to measure birefringence. It is a periodic reflector made up of periodically spaced zones physically formed in or on a section of fiber. The spacing is determined to have a refractive index slightly higher than the fiber core. That spacing reflects a narrow range of wavelengths while transmitting others. FIG. 3 shows conceptually a resonant reflection of a light wave from a Bragg grating. The amplitude of the sum of reflected waves changes linearly with the number of reflections. The frequency of reflection is related to the phase velocity of the transmitted light. The phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the velocity at which the phase of any one frequency component of the wave will propagate. In other words, one particular phase of the wave (for example the crest) travels at the phase velocity. (Recall that phase velocity and group velocity are different).
The two polarization modes of a PM fiber have different effective indices of refraction. Thus, they have different propagation constants within the fiber and have different peak reflection wavelengths. Because the electric fields in the two polarization modes have different wavelengths, the same reflector causes the two electric fields to reflect at different light frequencies.
Reflections in a fiber are naturally caused as a result of Rayleigh scatter. Rayleigh scatter in an optical fiber is a spatially distributed density function with little polarization dependence. Therefore, the random but fixed spectra, (i.e., the intensity of the scattering as a function of frequency), of PM fiber segments exhibit the same splitting of the spectra for the two polarization modes as observed with a Bragg grating. In the case of Rayleigh scatter, the splitting can determined using autocorrelation and cross-correlation functions of the measured reflected scatter. These functions can be determined by calculating the real-valued amplitude spectrum of a section of fiber and performing real-valued auto-and/or cross-correlations, or by multiplying the complex conjugate of measured complex reflection amplitude vs. fiber distance data obtained for a section of PM fiber using OFDR with another predetermined set of complex amplitude vs. distance data. The spectral separation of the calculated peaks is a measure of the local beat length of the fiber from which a measure of local fiber birefringence can be determined.
Based on these observation and determinations, the inventors determined a way to compute birefringence of a segment of a waveguide at a particular waveguide location by computing the autocorrelation of reflection spectrum associated with a particular location along the waveguide. To perform that calculation, an apparatus measures a complex response of a spectral reflection of the waveguide at a delay corresponding to the particular location along the waveguide. Non-limiting example apparatus include an OFDR or an optical low coherence reflectometer (OLCR). Then an autocorrelation function is determined using either of the methods just described, and the beirefringence is then calculated based on the distance between side and main autocorrelation peaks.
In an example where the waveguide is a PM fiber, light is coupled into two modes (fast and slow) of the PM fiber. The spectral response of the fiber segment which includes the two polarization modes is measured, e.g., using OFDR, OLCR, etc. The autocorrelation of the spectral response of a segment of fiber is then calculated. The spectral (wavelength) shift from the main autocorrelation peak to a side autocorrelation peak, corresponding to one of the two polarization modes of the PM fiber, is determined. The spectral shift or a percentage shift is multiplied by an average index of refraction to determine birefringence of the fiber segment.
Birefringence can be used to measure axial strain and/or temperature. Using Rayleigh scatter to determine birefringence rather than Bragg gratings offers significant advantages. First is reduced cost because Bragg gratings typically each cost hundreds of dollars. Second, the Rayleigh scatter measurement permits birefringence measurements at every location in the PM fiber, not just at predetermined locations. Freed from having to insert expensive gratings at specific measurement points along a fiber, many more measurement points may be used. Third, the process of physically “writing” a Bragg grating into optical fiber, in addition to being time consuming, often compromises the strength and integrity of the fiber. Those compromises are avoided using the Rayleigh scatter approach.
In one detailed example implementation, the reflected light intensity of a PM fiber as a result of Rayleigh scattering is measured using an OFDR or other swept laser system. The measured light intensities for the s and p polarization modes is preferably linearized using reference interferometer data. The linearized s and p light intensity data are then Fourier transformed into an array of complex data. The s and p complex data relating to a specific segment at a particular location along the fiber are extracted from the array. The extracted s and p data are Fourier transformed into the frequency domain, and the amplitude of the complex number at each point in the each of the s and p arrays is calculated. The vector sum of the two amplitude arrays is calculated to form a single amplitude spectrum, and the mean of the spectrum is removed. The autocorrelation of the amplitude spectrum is then determined resulting in a main autocorrelation peak and two side autocorrelation peaks for the s and p polarization modes. From the autocorrelation, the distance is determined from the center spectral peak to one of the s or p side peaks. The birefringence is then calculated for that location on the PM fiber based on the distance to the side peak.